Nuclear quadrupole resonance (NQR) is a solid-state radio frequency spectroscopic technique that can be used to detect compounds which contain quadrupolar nuclei, a requirement fulfilled by many high explosives and narcotics. Unfortunately, the low signal-to-noise ratio (SNR) of the observed signals currently inhibits the widespread use of the technique, thus highlighting the need for intelligent processing algorithms. In earlier work, we proposed a set of maximum likelihood-based algorithms enabling detection of even very weak NQR signals. These algorithms are based on derived realistic NQR data models, assuming that the (complex) amplitudes of the NQR signal components are known to within a multiplicative constant. However, these amplitudes, which are obtained from experimental measurements, are typically prone to some level of uncertainty. For such cases, these algorithms will experience a loss in performance. Herein, we develop a set of robust algorithms, allowing for uncertainties in the assumed amplitudes, showing that these offer a significant performance gain over the current state-of-the art techniques.